At the end of my last post I wrote about how I saw an article here crows titled ‘Recursive sequence generation in crows’, what it stated next piqued my interest ‘Recursion, the process of embedding structures within similar structures, is often considered a foundation of symbolic competence and a uniquely human capability.’ Other articles had more clickbait in their headlines, one stating ‘Crows Perform Yet Another Skill Once Thought Distinctively Human’, here and whilst this claim is not fully endorsed by all scientists I got to thinking about what I know of the Corvids and how this recursivity might be linked to their capacity for learning from experience. I wondered, given the frustration expressed in my last post about the difficulty in describing doing, and the proposal that experiential learning could be recursive, and the proposal that recursive thinking is based on language, and the observation that crows don’t talk, I wondered what it was in the experience of the crow that could produce recursive thinking.
So this post and some following posts will explore this through applied research and art as research with a view to applying ideas of recursivity to art making and experiential learning. The intention is to engage in subjective research, to use my own and other people’s observations along with art making to help me develop ideas through the action of making stuff and attending to what I make and what happens when I make it. This does not render an objective outcome in a scientific or empirical sense but it does render objects which provide opportunities for reflection and thus render personal insight and subjective knowledge. Outcomes are subjective, situational, experiential, embodied, emergent and multi-modal. As research, this will be generative and performative1. I hope it will make something happen.
Observing Doing
As part of my current outdoor as art practice, I walk a lot locally, I like the outdoors outside my front door and enjoy making art there. In my walking and my art making I have become quite attached to a local rookery. Through observation and reading, I came to realise the local rooks had culture. They had a form of collective knowledge learned from experience and shared. For example, in the winter I observed that they all left at dawn to feed remotely. They settled in a tree then set off en-masse to some remote destination. Normally they fed locally. I suspect they left for the Solway when the fields nearby were frozen solid. As a maritime environment, the ground freezes by the sea last. On my travels, driving as part of my day job, on frozen days I saw rooks feeding by the Solway in large numbers, but they were not there on warmer, unfrozen days. My hypothesis was that the local flock probably had birds with memories of feeding remotely on frozen days and these birds led the whole flock to feed. Memories of past events are seen as an aspect of recursive thinking enabling planning for future events or enacting plans for alternative actions in the present.
Describing Doing
In the aforementioned research, crows are shown to possess the power of recursive thinking. This is proposed to be a skill previously only seen in humans by virtue of being expressed through language. The implication being that crows don’t talk so how can they possess recursion as a skill. Central to the research was the act of bracketing, of seeing one pattern within another pattern. Crows were shown to be able to see the pattern within the pattern below with brackets within brackets.
This is said to relate to recursion emerging through our capacity to use language to embed one idea within or express one idea as another. Much of this relates to the work of Noam Chomsky. Chomsky explains linguistic recursion as something that occurs when a grammatical sentence, which includes a noun or noun phrase and a verb, might or might not contain another sentence. Again at its core recursion is the idea of perceiving one thing within or through another thing. Extended, this leads to ideas of language, empathy, imagination, planning, art, memory, culture, science and maths. The idea of symbolic thought, thinking beyond the here and now of animals. So crows thinking recursively intrigued me and delighted me.
I got to thinking about how my observation of my local rooks and crows suggests they are very familiar with one thing within another thing. I believed they could have a form of embodied recursivity. As a dramatherapist and experiential educator this interests me.
Crow Talk
When I walk locally I often see a crow and when she calls I hear other crows nearby which I cannot see. My supposition is that individual birds use calls to locate where other crows are. Thus they are aware of themselves as a thing within another thing, the bigger thing being them as a group or flock. They are social birds, specially the rooks, and their experience of their vocalisations will almost always be of themselves vocalising in relation to other birds’ vocalisations. One could imagine the call of one crow as a word within a bigger sentence uttered by the flock, but this is spatial and embodied not sequential and spoken like we speak.
In my initial research relating to me checking if I was understanding recursion correctly, I found that the idea of recursion cropped up in a broad range of settings. It recurred within maths, logic, biology, ecology, linguistics, philosophy, media studies, code and programming, art, literacy and creative writing, psychology and neuroscience including studies of consciousness, evolution and ontogeny, aesthetics, fractals and chaos theory, and that was in just one google search.
My interest is in experiential learning and art making as a form of experiential learning. So whilst in all this I could find no direct references to experiential learning and recursion, there was enough to provide material to connect recursion to experiential learning and art making. The range of references suggested a phenomenon that could connect many different things, which interests me as this suggests a phenomenon which could be at the root of many other phenomena. A key to art as research to explore and express personal experience is its multimodal use, exploring one thing through many artforms to see patterns, connections and exclusions. Art making is seeing one thing through another thing which suggests a core recursive function.
A Plan For a Direction of Travel
So my plan is to use basic research approaches, document searches and reading alongside art making as personal subjective research to explore and develop my understanding of recursion. This will be posted on my blog, but because a blog has the most recent post first, and this journey may be useful to be seen as going from it’s departure to it’s destination and not the reverse, I will put up pages showing the journey in it natural order. Because it is my belief that art making and/as experiential learning is intrinsically adventure, there will be no fixed destination. From the little I had read, I could immediately see that recursive processes are the same. A mathematical sequence has a fixed formula, often with an end point. But the recursivity exists as a process, moreover, it exists ‘in process.’ The formula makes some thing change. The recursive formula in maths could seem to be as far as you can get from art making and experiential learning, but each iteration of the formula derives its outcome from the previous iteration. It is cyclic like it learns from experience. Like art making it is a difficult thing to describe in words.
One definition of recursion (of many) is that recursion is a thing that defines itself by it’s own definition. here It is described as exhibiting self-similarity. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function. One example of recursivity brought together the aesthetics of art and geometry and a philosophical ideal for ancient Greece, the golden mean. In my training as a dramatherapist we put great emphasis on the archetype and the symbol in myth and storytelling. But with a background in science, I could see that the emergence of Euclid and Pythagoras also relied on the archetype and the symbol but through maths and geometry. Euclid worked out basic geometry and expressed it through his book Elements which was used as a core text until the 19th C. It is plausible that the work was done with nothing more than a compass and line in the sand on the floor, like at a campsite or like on a blank canvas. It was plain that the golden mean made itself from scratch. You start with a straight line, divide it into three, use a compass to make a right angle and define the section so AB/AS = AS/SB = 1.618… Yet the golden mean is found in nature, art, science, music theory, architecture, on and on. It is deeply self-similar and seems to recur in many diverse settings.
Doing Doing
What struck me was that recursion is a thing made in the making, it is a doing thing that remains elusive for words, it is as the saying goes, a path made in the walking of it, the principle of Dao as stated by Zhuangzi. So for my starting point I embarked on a path of making some thing, or numbers of things and work multi-modally. I want to also use poetry and story as if crow could inhabit recursivity, to show how crows subjective experience may include recursivity. I want to see if I could make the golden mean with a compass and a ruler, or more specifically, have the golden mean make itself facilitated by me. I want to do this through art making but also dig through more formal research descriptors. I want to see where this intended path will take me. I start with direction not destination.
Given that my initial interest was captured by the nature of crows I decided to work with language, but through poetry and imaginative writing to better express my ideas about recursion and how crows could experience and embody recursion without using words. This would be an experiment to see if a creative process could be used to explore and express the embodied experience of crows as recursion. This would, like I said, not be an alternative to scientific research, but an adjunct, an act of performative research to describe in a creative form what the science expressed in quantitative form. A subjective re-viewing of the thing the science showed us. The subjective object.
- Barrett and Bolt; Practice as Research – Approaches to Creative Arts Enquiry – Introduction. ↩
Moving Space 